What are the solutions to the equation 6t=-3t^2+75t+150 ?

The solutions to the equation 6t=-3t^2+75t+150 are t=-2,t=25

Find the zeros of 6t=-3t^2+75t+150

The zeros of 6t=-3t^2+75t+150 are t=-2,t=25

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6 t = - 3 t^{2} + 75 t + 150

t = - 2, t = 25

Solution steps

6 t = - 3 t^{2} + 75 t + 150

Switch sides

- 3 t^{2} + 75 t + 150 = 6 t

Move

6 t

to the left side

- 3 t^{2} + 69 t + 150 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 69 \pm 6 9 ^{2} - 4 ( - 3 ) \cdot 150}{2 ( - 3 )}

6 9^{2} - 4 (- 3) \cdot 150 = 81

t_{1, 2} = \frac{- 69 \pm 81}{2 ( - 3 )}

Separate the solutions

t_{1} = \frac{- 69 + 81}{2 ( - 3 )}, t_{2} = \frac{- 69 - 81}{2 ( - 3 )}

t = \frac{- 69 + 81}{2 ( - 3 )} : - 2

t = \frac{- 69 - 81}{2 ( - 3 )} : 25

The solutions to the quadratic equation are:

t = - 2, t = 25

y, x^{2} - 12 x y + y^{2} = 70

0 = 2 x^{2} - 10 x

x^{2} = 3 x - 15

- 8 x^{2} = - 1152

9 x^{2} = 6 x - 1

What are the solutions to the equation 6t=-3t^2+75t+150 ?
The solutions to the equation 6t=-3t^2+75t+150 are t=-2,t=25
Find the zeros of 6t=-3t^2+75t+150
The zeros of 6t=-3t^2+75t+150 are t=-2,t=25